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Solving Systems Using Matrices

Solving Systems Using Matrices. Section 7.2 & 7.3. Matrix. Row x Column. ROW. COLUMN. Matrix Equation. a x + b y = c d x + e y = f. X. A. B. Solving Matrix Equations. A∙X = B A -1 (A ∙ X) = A -1 (B) X = A -1 B. 2 nd , x -1 → EDIT Enter in matrix A & B

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Solving Systems Using Matrices

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  1. Solving Systems Using Matrices Section 7.2 & 7.3

  2. Matrix • Row x Column ROW COLUMN

  3. Matrix Equation ax + by = c dx + ey = f X A B

  4. Solving Matrix Equations A∙X = B A-1(A∙X) = A-1 (B) X = A-1B

  5. 2nd, x-1 • → EDIT • Enter in matrix A & B • 2nd, x-1 • Select Matrix [A] • Press x-1 • 2nd, x-1 • Select Matrix [B] • ENTER

  6. Ex) Solve using a matrix equation 2x + y = 10 x – 2y = -5

  7. Reduced Row Echelen Form • A matrix with only leading 1’s and 0’s everywhere else

  8. Solving using “ rref ” ax + by = c dx + ey = f 2nd, x-1 → MATH rref([A])

  9. x = r y = s

  10. Ex. Solve the system below by putting it into reduced row echelon form:

  11. -2 2 -4 -3 -2R1 + R2

  12. R1 + R3

  13. Switch R2 and R3

  14. 0 -3 3 -12 -3R2 + R3

  15. - ½ R3

  16. Solve using the given method Substitution Matrices 1. y = -2x + 4 2. 5x + 2y = 8 y = -2x - 1 x – y = 10 3. 2x + y = 2 4. y = -2x – 4 -2x + 2y = 10 5x + 3y = -6 { { Elimination Graphing { {

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